In this paper, we study the full statistics of photons transmitted through an optical cavity coupled to nanomechanical motion. We analyze the entire temporal evolution of the photon correlations, the Fano factor, higher moments of the photon distribution, and the effects of strong laser driving. In the regime of single-photon strong coupling, this allows us to predict interesting effects such as a transition from antibunching to bunching for larger observation time intervals and photon avalanches triggered by multi-photon absorption.